Family of simultaneous methods of Hansen-Patrick's type

Authors:
M. S. Petković;T. Sakurai;L. Rančić
Affiliations:
Faculty of Electronic Engineering, University of Niš, Beogradska 14, 18000 Niš, Serbia and Montenegro;Institute of Information Science and Electronics, University of Tsukuba, Tsukuba 305-8773, Japan;Faculty of Electronic Engineering, University of Niš, Beogradska 14, 18000 Niš, Serbia and Montenegro
Venue:
Applied Numerical Mathematics
Year:
2004

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Abstract

A one parameter family of iterative methods for the simultaneous determination of all (simple or multiple) complex zeros of a polynomial, based on a cubically convergent Hansen-Patrick's family, is considered. The proposed class of methods is adapted for the determination of simple zeros of a class of analytic functions which have only simple zeros inside a simple smooth closed contour in the complex plane. The presented convergence analysis shows that the order of convergence of the considered tamily is four. Numerical examples and a short description of the implementation on parallel computers are also given.